Walks along the branch lines in Devon and Cornwall (linear and circular), with downloadable instructions.  This site is run by the Devon and Cornwall Community Rail Partnership.  

The Exe Explorer Leaflet, on this web page, describes the Exe Estuary Trail, which runs along the the Exe Estuary, served by the Avocet Line, from Exeter to Exmouth.

Created by steering group member Steve Melia, this page includes downloadable gpx files for station-to-station walks (and some involving buses) in a wide radius around Bristol.

This web page has three rail walks in Devon and information about others in other parts of the country.

Walks from and between the stations along the Severn Beach Line from Bristol (linear and circular).  Run by the Friends of Bristol Suburban Railways. 

Walks from the stations in Dorset, linear and circular.  Some of them return by bus.

The Wessex Wanderers lead guided group walks from stations on the line between Bristol and Weymouth.

This website has detailed information on hundreds of walks around the country, including several in Southwest England. (Linear and circular)